Max Cuts in Trianglefree Graphs
Abstract
A wellknown conjecture by Erdős states that every trianglefree graph on $n$ vertices can be made bipartite by removing at most $n^2/25$ edges. This conjecture was known for graphs with edge density at least $0.4$ and edge density at most $0.172$. Here, we will extend the edge density for which this conjecture is true; we prove the conjecture for graphs with edge density at most $0.2486$ and for graphs with edge density at least $0.3197$. Further, we prove that every trianglefree graph can be made bipartite by removing at most $n^2/23.5$ edges improving the previously best bound of $n^2/18$.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.14179
 Bibcode:
 2021arXiv210314179B
 Keywords:

 Mathematics  Combinatorics;
 05C35
 EPrint:
 This is an extended abstract submitted to EUROCOMB 2021. Comments are welcome